Standard basis vectors -application of scalar multiplication, Mathematics

Assignment Help:

Standard Basis Vectors Revisited

In the preceding section we introduced the idea of standard basis vectors with no really discussing why they were significant.  We can now do that.  Let us start with the vector 

a = (a1, a2, a3)

We can make use of the addition of vectors to break this up as follows,

a = (a1, a2, a3)

= (a1, 0, 0) + (0, a2, 0) + (0, 0, a3)

By using scalar multiplication we can further rewrite the vector like,

a = (a1, 0, 0) + (0, a2, 0) + (0, 0, a3)

= a1 (1,0,0) + a2 (0, 1, 0) + a3 (0,0,1)

At last, notice that these three new vectors are just the three standard basis vectors for three dimensional space.

(a1, a2, a3) = a1i + a2j +a3k

Thus, we can take any vector and write out it in terms of the standard basis vectors.  From this point on we will make use of the two notations interchangeably so ensure that you can deal with both notations.


Related Discussions:- Standard basis vectors -application of scalar multiplication

Parallelogram, fig angles of a irregular polygons exterior and interior .

fig angles of a irregular polygons exterior and interior .

How many pages must he read before he takes a break, Joey has 30 pages to r...

Joey has 30 pages to read for history class tonight. He decided in which he would take a break while he finished reading 70% of the pages assigned. How many pages must he read befo

How many hours does dee work, Susan begins work at 4:00 and Dee starts at 5...

Susan begins work at 4:00 and Dee starts at 5:00. They both finish at the similar time. If Susan works x hours, how many hours does Dee work? Since Susan started 1 hour before

Obtain the number of significant modes, On the Assessment page for the modu...

On the Assessment page for the module Moodle site you will find five frequency response functions for the frequency range 20 to 100 Hz in the EXCEL spreadsheet "FRF_Data". These a

Ratio, how to do them?

how to do them?

Differentiate exponential functions, Differentiate following functions. ...

Differentiate following functions. (a)    R ( w) = 4 w - 5 log 9 w (b)   f ( x ) = 3e x + 10x 3 ln x Solution :  (a) It will be the only example which doesn't includ

Example of learning constructing tables versus rote , Maya says thafl for i...

Maya says thafl for instance, to help the children of Class 2 construct the '5 times table', she uses their hands. Each child counts how many fingers on one hand, and then how ma

How many different combinations could she form these item, Wendy has 5 pair...

Wendy has 5 pairs of pants and 8 shirts. How many different combinations could she form with these items? Multiply the number of choices for each item to find out the number of

How do you traverse a binary tree, How do you traverse a Binary Tree?  Desc...

How do you traverse a Binary Tree?  Describe Preorder, Inorder and Postorder traversals with example.     Ans: Traversal of tree means tree searching for a aim. The aim may be

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd